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Sine Formula to Find the Area of a Triangle

What we want to do in this lesson is look at a formula for the area of a triangle using trigonometry.

Now you’d all know the formula for the area of a triangle as half the base times the perpendicular height. But can we use our trigonometry to find the area of a triangle without knowing the perpendicular height? Yes we can.

What we’re going to do now, is to use a formula for the area where you don’t have to know the height of the triangle but you do need to know the lengths of the two sides and the size of the angle between them.

For example, in the triangle ABC, we’re given the length of two sides as 12 and 13 units, and the angle between them as 40 degrees. This would enable you to find the area. In this lesson we won’t be looking at how to derive this area rule but if you want to follow this up, you can find out in a textbook or on the internet.

Our area rule says this, “The area of a triangle is half the product of any two sides of the triangle times the sign ratio of the angle between the two sides.”

Let’s look at what this means in a general example. In this triangle ABC, we can say the area of the triangle would be half A times B times the sin of angle C.

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